By Bernard Kolman; Arnold Shapiro

A latest method of university algebra is supported through not obligatory snap shots calculator fabric

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Extra info for College algebra

Sample text

Equality satisfies these basic properties reflexive property symmetric property transitive property substitution property D There is a onc-t�ne correspondence between the set of all real numbers and the set of all points on the real number line. That is, for every point on the line there is a real number and for every real number there is a point on the Jine. D Algebraic statements using inequality symbols have straightforward geometric interpretations using the real number line. For example, a < b says that a lies to the left of b on the real number line.

A b=a-b --c c c For example, 3_ _ 2_ _ 4_ _ s_ = 2 - 4 + s = _ + x- 1 x- 1 x- 1 x-1 x- l To add or subtract rational expressions with different denominators, we must first rewrite each rational expression as an equivalent one with the same denom- 34 THE FOUNDATIONS OF ALGEBRA inator as the others. Although any common denominator will do, we will con­ centrate on finding the least common denominator, or LCD, of two or more rational expressions. We now outline the procedure and provide an example.

5 (-2,x2)S 1 . 19. 16. x" 20. '+ 24. 3 (r4)2 27. r + 1)7 31 . 2° + r 1 35. 3-41 39. y I 43. (32)2 -� 2 47. Fl 5 1. (3a-2b-3)-2 b-2 55. 3a5 9a-4b2 59. (a - 2b2)- 1 63. a-a-11 -+ bb--11 2 . 4 28. 32. 36. 40. -=6 � 44. 48. 52. 56. 60. 64. x12 3 (r)S • x4 14. 17. x3" . 18. c-2rc-2j" 21. ( 22. (x2)3(y2)4(x3)7 (�f 2b)4 26. (-2aab2)3 25. (¥y3)n [(3b + 1)5)5 (-3 29. a2b3)2n 30. (-�a2b3c2r � (y ) 2- 1 33 . 3+ 1)0 (-3)-3 x-s 38. -x-s 37. (-x)3 41. 5-35S 42. 4y5y-2 (2a)-6 45. (x-3)-3 46. r• 49 x2yy-3-2 50.